What is the least number of square pieces into which a cardboard, 13 ft long 8 ft wide, can be cut?
I drew 6
8*8
5*5
3*3
2*2
two 1*1
To determine the least number of square pieces into which the cardboard can be cut, we need to find out the size of each square piece.
The length of the cardboard is 13 ft and the width is 8 ft. To find the size of the square piece, we need to find the greatest common divisor (GCD) of the length and width.
GCD(13, 8) = 1
So, the size of each square piece will be 1 ft by 1 ft.
Now, to find the number of square pieces, we need to divide the total area of the cardboard by the area of each square piece.
Total area of the cardboard = length × width
Total area = 13 ft × 8 ft = 104 ft²
Area of each square piece = side × side
Area of each piece = 1 ft × 1 ft = 1 ft²
Number of square pieces = Total area ÷ Area of each piece
Number of square pieces = 104 ft² ÷ 1 ft² = 104
Therefore, the least number of square pieces into which the cardboard can be cut is 104.
To determine the least number of square pieces into which a cardboard can be cut, we need to find the greatest common divisor (GCD) of the length and width.
Step 1: Find the GCD of the length and width
The length is 13 ft, and the width is 8 ft. To find the GCD, we can use the Euclidean algorithm.
We start by dividing the larger number by the smaller number and find the remainder:
13 ft ÷ 8 ft = 1 remainder 5 ft
Now, we divide the divisor from the previous step (8 ft) by the remainder (5 ft):
8 ft ÷ 5 ft = 1 remainder 3 ft
Continuing the process:
5 ft ÷ 3 ft = 1 remainder 2 ft
3 ft ÷ 2 ft = 1 remainder 1 ft
2 ft ÷ 1 ft = 2 remainder 0 ft
Since we reached a remainder of 0, the GCD is the divisor from the last step, which is 1 ft.
Step 2: Calculate the total number of square pieces
To find the minimum number of square pieces, we need to divide the length and width by the GCD and multiply the results:
13 ft ÷ 1 ft = 13
8 ft ÷ 1 ft = 8
Multiplying the results:
13 × 8 = 104
Therefore, the least number of square pieces into which the cardboard can be cut is 104.